Question

Swati can row her boat at a speed of $5km/hr$ in still water. If it takes her $1$ hour more to row the boat $5.25km$ upstream than to return downstream, find the speed of the stream.

Answer 1

Let the speed of the stream be $x$ km/hr

Speed of the boat upstream$=(5-x)$km/hr

Speed of the boat downstream$=(5+x)$ km/hr

Time taken for going $5.25km$ upstream $=\frac{5.25}{5-x}hours$

Time taken for going $5.25km$ downstream $=\frac{5.25}{5+x}hours$

Obviously, time taken for going $5.25km$ upstream is more than the time taken for going $5.25km$, downstream
It is given that the time taken for going $5.25km$, upstream is $1$ hour more than the time taken for going $5.25$ downstream

$\therefore \frac{5.25}{5-x}-\frac{5.25}{5+x}=1$

$\Rightarrow 5.25\{\frac{1}{5-x}-\frac{1}{5+x}\}=1\Rightarrow \frac{21}{4}\left(\frac{5+x-5+x}{(5-x)(5+x)}\right)=1$

$\Rightarrow \frac{21}{4}\times \frac{2x}{25-x^2}=1\Rightarrow \frac{21}{2}\times \frac{x}{25-x^2}=1$

$\Rightarrow 2x^2+21x-50=0$

$\Rightarrow x(2x+25)-2(2x+25)=0\Rightarrow (2x+25)(x-2)=0$

$\Rightarrow x-2=0,2x+25=0$

$\Rightarrow x=2[\because x\ne \frac{-25}{2}]$

$\therefore$ speed of the stream $=2km/hr$